Enter the coefficients of a polynomial and instantly get its indefinite integral — plus the definite integral if you give bounds.
Polynomial Integral Calculator
How It’s Calculated
The power rule for integration reverses differentiation: ∫ a·xⁿ dx = (a/(n+1))·x(n+1) + C, adding 1 to the exponent and dividing by the new exponent. The constant C exists because any constant’s derivative is 0, so integration can never recover it — it’s always left as an unknown. For a definite integral between two bounds, this constant cancels out, so this tool evaluates F(upper) − F(lower) directly when you provide both bounds.
Worked Example
For f(x) = 6x² + 10x − 4: ∫ f(x) dx = 2x³ + 5x² − 4x + C. Evaluated from 0 to 2: F(2) − F(0) = (16+20−8) − 0 = 28.
Frequently Asked Questions
Q: Why does the constant C disappear in a definite integral?
Because F(upper) + C minus F(lower) + C leaves the two C terms cancelling out — the constant never affects the difference between two values of the same antiderivative.
Q: Does this handle 1/x or trigonometric terms?
Not this tool — it’s built specifically for polynomial terms using the power rule. 1/x integrates to ln|x|, which follows a different rule entirely, covered separately in the Integrals chapter.
This is the reverse of the Polynomial Derivative Calculator, and both come from the same 2nd PUC Integrals chapter. Try the Derivative Calculator →